Abstract

Purpose:
We generated a model of eye growth and tested it against an eye known to develop abnormally, one with a history of retinopathy of prematurity (ROP).

Methods:
We reviewed extant magnetic resonance images (MRIs) from term and preterm-born patients for suitable images (n = 129). We binned subjects for analysis based upon postmenstrual age at birth (in weeks) and ROP history ("Term" ≥ 37, "Premature" ≤ 32 with no ROP, "ROP" ≤ 32 with ROP). We measured the axial positions and curvatures of the cornea, anterior and posterior lens, and inner retinal surface. We fit anterior chamber depth (ACD), posterior segment depth (PSD), axial length (AL), and corneal and lenticular curvatures with logistic growth curves that we then evaluated for significant differences. We also measured the length of rays from the centroid to the surface of the eye at 5° intervals, and described the length versus age relationship of each ray, L(ray)(x), using the same logistic growth curve. We determined the rate of ray elongation, E(ray)(x), from L(ray)dy/dx. Then, we estimated the scleral growth that accounted for E(ray)(x), G(x), at every age and position.

Results:
Relative to Term, development of ACD, PSD, AL, and corneal and lenticular curvatures was delayed in ROP eyes, but not Premature eyes. In Term infants, G(x) was fast and predominantly equatorial; in age-matched ROP eyes, maximal G(x) was offset by approximately 90°.

Conclusions:
We produced a model of normal eye growth in term-born subjects. Relative to normal, the ROP eye is characterized by delayed, abnormal growth.

Figures

The MRI analysis procedure. (A) Sample MRI section exported from Voxar3D. The image must be rotated such that the plane of the ciliary body (brown line), indicated by the operator (red crosshairs), is parallel to the horizontal image axis. (B) Following image rotation, the first derivative of the brightness profile of the axis of the eye (plotted to the left) was obtained. Troughs and peaks in this profile (circles), which corresponded to the cornea, anterior lens, posterior lens, and retina, were automatically identified. (C) From the positions of the identified features, ACD, LT, and PSD were calculated. Corresponding surfaces also were identified (red, cornea; green, lens; yellow, retina). (D) Circles were fit to the anterior and posterior cornea (not shown) and lens (shown) to determine radii of curvature. (E) Rays from the centroid of each eye (red X) were measured to the inner edge of the eye (magenta line) every 5°. (F) This process was repeated for the lens.

Demonstration of the calculation of minor angles (Δminor, Equation 6b) to 10 preselected points, φ, from two starting positions, θ: one at the direct posterior of the eye (θ = 0°, left) and one 45° nasal (θ = 315°, right). Angles are measured counterclockwise from the posterior pole around the centroid (red X) of a model eye (thick black line); the positions of the same 10 values of φ are indicated in both panels by blue line segments. As shown, Δminor (green arcs and points) is computed as the smallest angle from φ to the line connecting the centroid and θ (brown line). Growth (Gθ', Equation 6a) is measured all around the globe at every θ, accounting for contributions (Ecirc,φ) from every φ (not just the 10 shown above) scaled by Δminor (Equation 6b).

Figure 3

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The SE refraction, from the…

Figure 3

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The SE refraction, from the 75 subjects for which this information was available,…

Figure 3

The SE refraction, from the 75 subjects for which this information was available, plotted as a function of postmenstrual age. The mean (blue line) and 5th to 95th prediction interval (pale shaded region) for “typical refraction” was obtained from Mayer et al. and the CLEERE study group. The green line is the fit of the Term data with Equation 1. The data from the eyes of two ROP subjects with the longest observed axial lengths (Fig. 5) are noted (yellow fills); these subjects were excluded from the fit and all subsequent analyses. Corrected age was calculated as the sum of PMA and 10/13ths of a year (i.e., 40 weeks).

Figure 4

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Measurements from both eyes of…

Figure 4

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Measurements from both eyes of every subject plotted as a function of PMA…

Figure 4

Measurements from both eyes of every subject plotted as a function of PMA for ACD, LT, PSD, and AL of the whole eye (which is the sum of the other three parameters and a small contribution of corneal thickness). The lines are fits of the data of the Term, Preterm, and ROP groups with Equation 1 with y0 fixed at 0.

Figure 5

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“Abnormality” scores for ACD, LT,…

Figure 5

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“Abnormality” scores for ACD, LT, PSD, and AL calculated by taking the difference…

Figure 5

“Abnormality” scores for ACD, LT, PSD, and AL calculated by taking the difference between each point (minuend) in Figure 4 and the point on the regression line for Term subjects at the same age (subtrahend). Lines plot the mean abnormality for the Term, Preterm, and ROP groups. The pale shaded region indicates the 5th to 95th prediction limit for Term abnormality.

Figure 6

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Measurements from both eyes of…

Figure 6

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Measurements from both eyes of every subject plotted as a function of PMA…

Figure 6

Measurements from both eyes of every subject plotted as a function of PMA for CC, ALC, PLC, and the ratio of the ASL to PSD (ASL/PSD). The lines are fits of the data of the Term, Preterm, and ROP groups with Equation 1 with y0 fixed at 0, except at the bottom right, where y0 was free to vary.

Figure 7

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“Abnormality” scores for CC, ALC,…

Figure 7

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“Abnormality” scores for CC, ALC, PLC, and the ratio of ASL to PSD…

Figure 7

“Abnormality” scores for CC, ALC, PLC, and the ratio of ASL to PSD (ASL/PSD). The pale shaded region indicates the 5th to 95th prediction limit for Term abnormality. Lines plot the mean abnormality for the Term, Preterm, and ROP groups.

Figure 8

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Model eye and lens cross-sections…

Figure 8

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Model eye and lens cross-sections from Term (green) and ROP (red) eyes at…

Figure 8

Model eye and lens cross-sections from Term (green) and ROP (red) eyes at the ages indicated. Preterm eyes were nearly indistinguishable from Term eyes and are excluded for clarity. Dots indicate the θs of maximal growth, G(x) (Equation 7). Areas of bright color on the eyes indicate regions for which the model indicated the highest growth, while black areas are those the model indicated were growing more slowly; brightness is normalized at each age to the areas of highest and lowest growth, but growth was overall slower at older ages (as evidenced by the decreasing change in size with increasing age).